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Symplectic Geometry and Quantization
 
Edited by: Yoshiaki Maeda Keio University, Yokohama, Japan
Hideki Omori Science University of Tokyo, Chiba Ken, Japan
Alan Weinstein University of California, Berkeley, Berkeley, CA
Symplectic Geometry and Quantization
eBook ISBN:  978-0-8218-7770-8
Product Code:  CONM/179.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Symplectic Geometry and Quantization
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Symplectic Geometry and Quantization
Edited by: Yoshiaki Maeda Keio University, Yokohama, Japan
Hideki Omori Science University of Tokyo, Chiba Ken, Japan
Alan Weinstein University of California, Berkeley, Berkeley, CA
eBook ISBN:  978-0-8218-7770-8
Product Code:  CONM/179.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1791994; 285 pp
    MSC: Primary 58; 81; Secondary 22; 46;

    This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants. The book provides insight into how these different topics relate to one another and offers intriguing new problems. Providing a look at the frontier of research in symplectic geometry and quantization, this book is suitable as a source book for a seminar in symplectic geometry.

    Readership

    Graduate students and researchers

  • Table of Contents
     
     
    • Articles
    • Michel Cahen, Simone Gutt and John Rawnsley — Some remarks on the classification of Poisson Lie groups [ MR 1319599 ]
    • Pierre Dazord — Lie groups and algebras in infinite dimension: a new approach [ MR 1319600 ]
    • J. J. Duistermaat — Equivariant cohomology and stationary phase [ MR 1319601 ]
    • E. Getzler — The Bargmann representation, generalized Dirac operators and the index of pseudodifferential operators on ${\bf R}^n$ [ MR 1319602 ]
    • Mikhail Karasev — Quantization by means of two-dimensional surfaces (membranes): geometrical formulas for wave-functions [ MR 1319603 ]
    • Mikhail Karasev — Geometric star-products [ MR 1319604 ]
    • Toshitake Kohno — Vassiliev invariants and de Rham complex on the space of knots [ MR 1319605 ]
    • Hiroshi Konno — Geometry of loop groups and Wess-Zumino-Witten models [ MR 1319606 ]
    • Tetsuya Masuda and Hideki Omori — The noncommutative algebra of the quantum group ${\rm SU}_q(2)$ as a quantized Poisson manifold [ MR 1319607 ]
    • Kentaro Mikami — Symplectic and Poisson structures on some loop groups [ MR 1319608 ]
    • Hitoshi Moriyoshi — The Euler and Godbillon-Vey forms and symplectic structures on ${\rm Diff}^\infty _+(S^1)/{\rm SO}(2)$ [ MR 1319609 ]
    • Yoshimasa Nakamura — A tau-function for the finite Toda molecule, and information spaces [ MR 1319610 ]
    • Hideki Omori, Yoshiaki Maeda and Akira Yoshioka — Deformation quantizations of Poisson algebras [ MR 1319611 ]
    • Kaoru Ono and Stephan Stolz — An analogue of Edmonds’ theorem for loop spaces [ MR 1319612 ]
    • Alan Weinstein — Traces and triangles in symmetric symplectic spaces [ MR 1319613 ]
    • Stanisław Zakrzewski — Geometric quantization of Poisson groups—diagonal and soft deformations [ MR 1319614 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1791994; 285 pp
MSC: Primary 58; 81; Secondary 22; 46;

This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants. The book provides insight into how these different topics relate to one another and offers intriguing new problems. Providing a look at the frontier of research in symplectic geometry and quantization, this book is suitable as a source book for a seminar in symplectic geometry.

Readership

Graduate students and researchers

  • Articles
  • Michel Cahen, Simone Gutt and John Rawnsley — Some remarks on the classification of Poisson Lie groups [ MR 1319599 ]
  • Pierre Dazord — Lie groups and algebras in infinite dimension: a new approach [ MR 1319600 ]
  • J. J. Duistermaat — Equivariant cohomology and stationary phase [ MR 1319601 ]
  • E. Getzler — The Bargmann representation, generalized Dirac operators and the index of pseudodifferential operators on ${\bf R}^n$ [ MR 1319602 ]
  • Mikhail Karasev — Quantization by means of two-dimensional surfaces (membranes): geometrical formulas for wave-functions [ MR 1319603 ]
  • Mikhail Karasev — Geometric star-products [ MR 1319604 ]
  • Toshitake Kohno — Vassiliev invariants and de Rham complex on the space of knots [ MR 1319605 ]
  • Hiroshi Konno — Geometry of loop groups and Wess-Zumino-Witten models [ MR 1319606 ]
  • Tetsuya Masuda and Hideki Omori — The noncommutative algebra of the quantum group ${\rm SU}_q(2)$ as a quantized Poisson manifold [ MR 1319607 ]
  • Kentaro Mikami — Symplectic and Poisson structures on some loop groups [ MR 1319608 ]
  • Hitoshi Moriyoshi — The Euler and Godbillon-Vey forms and symplectic structures on ${\rm Diff}^\infty _+(S^1)/{\rm SO}(2)$ [ MR 1319609 ]
  • Yoshimasa Nakamura — A tau-function for the finite Toda molecule, and information spaces [ MR 1319610 ]
  • Hideki Omori, Yoshiaki Maeda and Akira Yoshioka — Deformation quantizations of Poisson algebras [ MR 1319611 ]
  • Kaoru Ono and Stephan Stolz — An analogue of Edmonds’ theorem for loop spaces [ MR 1319612 ]
  • Alan Weinstein — Traces and triangles in symmetric symplectic spaces [ MR 1319613 ]
  • Stanisław Zakrzewski — Geometric quantization of Poisson groups—diagonal and soft deformations [ MR 1319614 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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